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Lecture Comments (2)

1 answer

Last reply by: Hira Javaid
Wed Oct 16, 2013 10:34 AM

Post by Callistus Elue on September 22, 2011

In Lecture 21, i.e Simple Harmonic Motion, I am not able to access the subtopics; Harmonic Oscillation Equation of Motion, Solution to the Equation, Period, Energy of Harmonic Oscillator and Pendulum. The video always goes back to the beginning of the Lecture once it finishes Derivative cos (Ax+b). How can I get over this challenge?

Simple Harmonic Motion

  • Upon displacing an objects attached to one end of a spring, the other end being fixed, by a distance x, a restoring force equal to –kx, where k is the force constant of the spring, acts on the body.
  • The force, being –kx, we can write Newton’s second law of motion as a differential equation. The solution of this differential equation gives oscillatory motion, or simple harmonic motion.
  • The time to make one complete cycle is the period.
  • In the spring-block system, the period of oscillation depends only on the mass of the block and the force constant of the spring.
  • In the spring-block system, the total mechanical energy is the sum of the kinetic energy of the block and the elastic energy of the spring.
  • The period of a pendulum depends only on the length of the pendulum and the value of g, the acceleration due to gravity.

Simple Harmonic Motion

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • (Six x)/x 0:09
    • (Sin x)/x Lim-->0
    • Definition of Sine
    • Sine Expressed in Radians
    • Example: Sin(5.73)
  • Derivative Sin(Ax+b) 12:14
    • f(x)=Sin(ax+b)
    • Sin(α+β)
  • Derivative Cos(Ax+b) 20:05
    • F(x)=Cos(Ax+b)
  • Harmonic Oslillation: Equation of Motion 26:00
    • Example: Object Attached to Spring
    • Object is Oscillating
    • Force Acting on Object F=m*a
    • Equation of Motion
  • Solution to The Equation of Motion 36:40
    • x(t) Funtion of time
    • x=Cos(ωt+ø) Taking Derivative
  • Period 50:37
    • Pull The Spring With Mass and Time t Released
    • Calculating Time Period =A cos(ωt - φ)
  • Energy of Harmonic Oscillator 55:59
    • Energy of The Oscillator
  • Pendulum 58:10
    • Mass Attached to String and Swing
  • Extra Example 1: Two Springs Attached to Wall
  • Extra Example 2: Simple Pendulum
  • Extra Example 3: Block and Spring Oscillation